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James Tobin on Overlapping Generations Models and the Microeconomic Foundations of Macroeconomics Reconsidered

James Tobin, les modèles à générations imbriquées et le réexamen des microfondations de la macroéconomie
Robert W. Dimand
p. 21-37

Résumés

L’économiste keynésien américain et prix Nobel James Tobin a choisi pour titre, pour sa contribution au numéro inaugural du Journal of Money, Credit and Banking, « A General Equilibrium Approach to Monetary Theory », alors que, pourtant, il était profondément critique de la version de l’analyse de l’équilibre général utilisé dans ce qui est aujourd’hui l’approche prévalente dans la modélisation d’équilibre général dynamique et stochastique. Il rejetait également l’idée que les modèles à générations imbriquées proposent des fondations, ancrées dans la théorie du choix, pour expliquer la détention de monnaie fiduciaire, niant ainsi que l’hypothèse que les agents détiennent de la monnaie fiduciaire car aucun autre actif existe soit moins arbitraire que de supposer que les coûts des transactions entre actifs sont non-nuls. Cependant, tout en rejetant les modèles à génération imbriquées en tant qu’explication de la raison pour laquelle les agents détiennent de la monnaie fiduciaire, Tobin, dans une série d’articles publiés entre 1967 et 1983 (dont certains coécrits avec Walter Dolde) introduit au sein des modèles à générations imbriquées le modèle du cycle de vie de la consommation et de l’épargne (dont il attribue les origines à un autre économiste de Yale, Irving Fisher). Cet article analyse les critiques de Tobin envers l’usage en macroéconomie de modèles d’équilibre général dynamique et stochastique et de modèles à générations imbriquées, ainsi que le sens de sa proposition d’une « approche d’équilibre général à la théorie monétaire » et sa contribution dans l’introduction du modèle du cycle de vie dans les modèles à générations imbriquées.

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1The American Keynesian economist and 1981 Nobel laureate James Tobin entitled his contribution to the inaugural issue of the Journal of Money, Credit and Banking “A General Equilibrium Approach to Monetary Theory” (1969) yet his vision of what constituted a general equilibrium approach to monetary economics contrasted sharply with what is meant by general equilibrium in the now widely influential dynamic stochastic general equilibrium (DSGE) approach to macroeconomics, which has become prevalent among New Keynesian as well as New Classical economists. New Classical economists, and commentaries such as Michel De Vroey’s History of Modern Macroeconomics from Keynes to Lucas and Beyond (2016), portray this contrast, controversially, as New Classical economists arguing for, and their Keynesian critics against, rigorous, explicit, logically consistent choice-theoretic, optimizing microeconomic foundations for macroeconomics. As part of his critique of the claims that New Classical economics provided logically consistent choice-theoretic microeconomic foundations for macroeconomics and that Keynesian economics did not do so, Tobin rejected claims that overlapping generations models (OLG) provided solid rational choice foundations for the holding and value of fiat money. Tobin (1980) was particularly dismissive, or even contemptuous, of the assertion that to assume that people hold fiat money because no other asset exists is in some sense less arbitrary than allowing the costs of transactions between fiat money and other assets to be strictly positive. He found the assumption that there are no other assets a flimsy alternative to either the Allais-Baumol-Tobin transactions demand for money or the Markowitz-Tobin portfolio balance analysis of demand for money as an asset. However, Tobin’s position on OLG modeling, and hence his position on choice-theoretic microeconomic foundations more generally, is frequently misunderstood. Far from rejecting OLG modeling in general, Tobin was an early adopter of OLG modeling in the context where he considered it appropriate, that of intergenerational wealth accumulation. What he rejected as inappropriate was the use of OLG modeling, combined with the assumption that no asset other than fiat money exists, to explain the existence and positive value of fiat money. Tobin’s version of a “general equilibrium approach to monetary theory,” including both his early adoption of OLG modeling and his critique of what he considered the misuse of OLG modeling to explain fiat money, set him apart from the other leading American Keynesians of his generation such as Robert Solow, Franco Modigliani or Lawrence Klein, even though these shared his more general skepticism about the New Classical/DSGE microfoundations project.

  • 1 In Yaari’s case, not just a colleague but a coauthor with Tobin at that time: Cass and Yaari (1966) (...)

2While emphatically rejecting OLG as the explanation of why people hold fiat money and why fiat money has value, Tobin, in a series of articles from 1967 to 1983 (some of them written jointly with his former student Walter Dolde), placed the life-model model of consumption and saving (which he traced back to an earlier Yale monetary economist, Irving Fisher) into the framework of Allais-Samuelson-Diamond OLG modeling, continuing a concern with the microeconomic foundations of aggregate saving and consumption that began with his 1947 Harvard doctoral dissertation. In the words of Willem Buiter, Tobin “pioneered the application of what is now referred to as the ‘Yaari-Blanchard’ version of the life cycle overlapping generations model to the study of important monetary and fiscal policy issues using realistic numerically calibrated versions of the model.” (Buiter, 2003, F585) Tobin selected Samuelson (1958), the foundational work of OLG modeling (since anglophone economists had not read Allais, 1947), and Cass and Yaari (1966), a key reconsideration of Samuelson’s OLG model written when Cass and Yaari were Tobin’s colleagues at the Cowles Foundation at Yale,1 for inclusion in Landmark Papers in Macroeconomics (Tobin, 2002). Tobin’s sweeping rejection of the use by Neil Wallace (1980) of OLG to explain the phenomenon of fiat money was not a rejection of the importance and usefulness of thinking in terms of overlapping generations models, but rather was a strongly held difference of opinion about the class of problems that OLG modeling could illuminate, a distinction recognized in Buiter’s memorial article on Tobin and noted briefly in the history of OLG modelling by Stephen Spear and Warren Young (Spear and Young, 2023) but by few others commenting on Tobin’s critique of Wallace. Tobin (1980) did not object to OLG models but to what he considered the misuse of OLG. He also embraced general equilibrium, in the sense of adding-up constraints and stock-flow consistency, and optimization, as with the trade-off between transactions costs and foregone interest in the Allais-Baumol-Tobin model of transactions for money or between risk and return in portfolio choice. His objection was to identifying general equilibrium, optimization and microfoundations with budget constraints that assumed the labor market always clears, so that agents can sell all their labor at the prevailing wage.

1. Tobin’s Critique of Neil Wallace’s OLG Explanation of the Existence and Value of Fiat Money

3James Tobin offered several rebuttals to the New Classical challenge to Keynesian economics (see Dimand, 2022 on Tobin’s exchanges with Robert Lucas, and Arnon, 2022; Ingrao, 2022; for a contrasting view, see De Vroey, 2016, 212-213, 218-224) as well as critical remarks in interviews (such as his interviews with David Colander, 1999 and Robert Shiller, 1999) but his fullest critique of the OLG portion of the New Classical microfoundations project was “Explaining the Existence and Value of Money” (Tobin, 1980; see also Tobin interviewed by Colander, 1999, 124). Tobin presented this at the Federal Reserve Bank of Minneapolis Conference on Models of Monetary Economics, December 7-8, 1978, as his discussant’s comment on a paper by the conference co-organizer, Neil Wallace of the University of Minnesota and of the Research Department of the FRB Minneapolis (Wallace, 1980). The University of Minnesota and the Minneapolis Fed had taken a leading role in the development of what came to be termed, for its roots in Chicago and Rochester as well as Minneapolis, “freshwater macroeconomics” based on rational expectations, market clearing and an appeal to explicitly choice-theoretic microeconomic foundations (see Sims, 1977 and Miller, 1994, the latter an anthology of articles from the Federal Reserve Bank of Minneapolis Quarterly Review, including five written or coauthored by Wallace). Kareken and Wallace (1980), in the proceedings of the 1978 conference, presented OLG models as providing rigorous microeconomic foundations for the existence and strictly positive real value of unbacked fiat money within that research program. Tobin, although he found OLG useful and insightful in other contexts, dissented emphatically.

4Wallace (1980), like Gale (1973), presented a model in which fiat money, a nonreproducible asset paying zero interest, was the only store of value available to transfer purchasing power from one period to another, the only means for people to save while young and working so that they could continue to consume while old and retired. If an interest-bearing asset was available, no one would hold fiat money in that model. Tobin (1980, 84) objected that “if a nonreproducible asset has been needed for intergenerational transfers of wealth, land has always been available. Quantitatively it has been a much more important store of value than money.”

5Tobin (1980, 84) found it “slightly ridiculous to identify as money the asset that the typical agent of the model would hold for an average of 25 years, say from age 40 to age 65 … The average holding period of a dollar of demand deposits is 2 days.” He noted the continued existence and holding of money in societies that had social security systems and interest-bearing assets or in which the net marginal product of capital has exceeded the growth rate of income. Tobin also denied that the typical life cycle of model of consumption-smoothing had just periods, saving followed by dissaving: people start out being supported by their parents, then take out student loans and, as they form households, mortgages, before saving for retirement. He insisted that although money was certainly a store of value, not all stores of value were money, only those that could serve as a medium of exchange and unit of account: “The traditional explanation of money is the division of labor, the daily recurring need to exchange specialized endowments or products for diversified consumption goods and services.” (Tobin, 1980, 86) What Wallace (1980) referred to as “money” did not serve as a medium of exchange and was by assumption the only available store of value. Consequently, in Tobin’s view, Wallace had only shown why people hold wealth, not why they hold fiat money, and had repeated, in somewhat different terminology, the explanation by Irving Fisher (1907; 1930) of why and how people choose to save (demand assets) to smooth their consumption across time periods, as illustrated by the two-period optimal consumption diagram of Fisher (1907, 409).

  • 2 Baumol and Tobin (1989) acknowledged that their square-root rule for transactions demand for househ (...)

6William Brock (1990, 281), surveying OLG modelling of fiat money in the Handbook of Monetary Economics, suggested that “One could argue that Tobin is interpreting a useful metaphor too literally” although some of Tobin’s objections were “hard to bypass.” But Tobin’s point concerned not whether the OLG metaphor was useful but what it was useful for. Tobin acknowledged that OLG models of fiat money capture one, but only one, crucial feature of financial assets that are not backed by convertibility at fixed rates into land or physical capital or commodities such as gold or silver: the value of such assets to the present generation depends on what it will be worth to the next generation, which depends on what it will be worth to the generation after that, and so on ad infinitum. Fiat money is an example of such a financial asset, but far from the only example. The OLG metaphor does not explain why people hold some of their wealth as fiat money when other assets pay strictly higher rates of return. Tobin pointed to other distinctive features of money as a means of payment and as an asset whose risk/return characteristics were not identical to those of other assets for which it was an imperfect substitute. Models of transaction demand for money such as Allais (1947, 238-241), Baumol (1952) and Tobin (1956) explained the holding of a zero-interest medium of exchange when bonds pay positive rates of interest by assuming that there is some cost per transaction of trading bonds for media of exchange to spend, at a very minimum the opportunity cost of a person’s time spent doing so.2 Tobin (1958a), extending the optimal portfolio diversification analysis of Markowitz (1952), looked to the tradeoff between risk and expected return to explain why people would hold part of their portfolio as zero (nominal) return and (in nominal terms) riskless fiat money and the rest in risky assets with a positive expected return. Allowing for money to be risky because of changes in its purchasing power, money would still have a place in an optimally diversified portfolio because its risk/return characteristics were not the same as those of other assets. To the objection that it was arbitrary to assume a lump-sum or proportional cost of transacting between bonds and the medium of exchange or to attribute to money a different risk/return profile from other assets, Tobin responded that it was even more arbitrary to impose the assumption that no assets could exist. He did not regard this response, refusing to abandon his previous approach to explaining money demand for an OLG approach, as unfairly “taking a useful metaphor too literally” as purporting to offer rigorous explicit foundations or, alternatively, as rejecting rigorous explicit foundations in favor of “implicit theorizing.”

7David Cass and Karl Shell, in “A Defense of a Basic Approach” written after the conference for inclusion in Kareken and Wallace (1980, 251-260), responded to Tobin by demonstrating that financial assets such as money are indeed stores of value, as if Tobin had questioned that. While arguing, contrary to what they termed “the rational expectations school,” that the OLG approach to modeling allowed for multiple equilibria where monetary policy matters, Cass and Shell objected to Keynesian economics, such as that of Tobin, as “not derived from consistent individual maximizing behavior” (Kareken and Wallace, 1980, 254; Cherrier and Saïdi, 2018, 430-431). Wallace professed himself unshaken in his conviction that the OLG metaphor had provided for the first time a rigorous basis for thinking about for the existence and positive value of fiat money yet his subsequent shift to seeking search-theoretic microeconomic foundations for the use of fiat money as a medium of exchange suggests an implicit acceptance of Tobin’s critique of the OLG metaphor as the explanation of fiat money (Altig and Nosal, 2013).

2. Tobin on Intertemporal and Intergenerational Analysis of Saving and Consumption

  • 3 As a Yale undergraduate, Peter Diamond worked with Tjalling Koopmans (see Diamond et al., 1962; Koo (...)

8Tobin firmly dismissed any OLG explanation for the existence and value of fiat money that depended on assuming that, perhaps because of legal restrictions, no other stores of value were available. Nonetheless, Tobin found OLG models useful for teaching and research concerning intergenerational wealth transfers, consumption-smoothing and monetary and fiscal policy. He did so from the early days of OLG analysis in the English-language literature, if not from the publication of Paul Samuelson (1958; Allais, 1947, Appendix II, was little known before Malinvaud, 1987), at least from that of Peter Diamond (1965), Menachem Yaari (1965), and David Cass and Yaari (1966), articles by a recent Yale graduate3 and by two Yale junior faculty, one of them (Yaari) a coauthor with Tobin. At the end of his career, Tobin selected Samuelson (1958) and Cass and Yaari (1966) for reprinting in Landmark Papers in Macroeconomics (Tobin, 2002). Buiter recalled:

Like all [Tobin’s] students, I learned to appreciate the versatility and power of the OLG model, which was used intensively in his graduate lectures. Even the simplest 2-period version provides a natural analytical framework for studying retirement saving and social security issues. Because it allows for at least one key demographic form of heterogeneity among consumers, it also represents a natural analytical vehicle for combining a Keynesian approach to the macroeconomic consequences of deficit financing and alternative social security systems—which requires heterogeneous consumers—with the explicit intertemporal optimizing approach Tobin so admired in Irving Fisher (1930). (Buiter, 2003, F592)

  • 4 Then as now, economists were less conscious of Fisher’s The Rate of Interest (1907) and usually una (...)
  • 5 Tobin (1967) did not cite Yaari (1965) or indeed, apart from mention of Fisher (1930, Chapter V), a (...)
  • 6 Simulation using calibration was undertaken actively at Yale following the arrival of Guy Orcutt as (...)

9Although usually thought of as a monetary economist, Tobin (1947) wrote his Harvard PhD dissertation on “A Theoretical and Statistical Analysis of Consumer Saving,” nominally supervised by Joseph Schumpeter but effectively self-supervised. Two decades later, it was an expert on the consumption function rather than on a monetary topic that he contributed to the International Encyclopedia of the Social Sciences (reprinted in Tobin, 1971-1996, Volume 2). Tobin critically examined the permanent income hypothesis of Friedman (1957), praising its elegant simplicity but asking “is it better to be simple than right?” (Tobin, 1958b, 124) In his dissertation and in early articles based on it, Tobin (1947; 1951; 1952) added an intertemporal dimension to the simple Keynesian consumption function by making saving a function of both income and wealth, so that saving in one period would affect saving in the next period by changing household wealth. With this altered specification of the consumption function, rising financial wealth could explain the apparent contradiction between cross-section and time-series estimation of the marginal propensity to consume. As part of the rediscovery and reevaluation of Irving Fisher by Yale economists on the centenary of Fisher’s birth, Tobin (1967) analyzed “Life-Cycle Saving and Balanced Growth,” linking his analysis to Fisher’s The Theory of Interest (1930).4 In Fisher’s analysis, agents smooth consumption with perfect credit markets so that the present discount value of expected lifetime earnings is the budget constraint for lifetime consumption, without consumption in a period depending on income in that period. Equilibrium is at the tangency of an individual’s indifference curve to the intertemporal budget constraint, with the marginal rate of time preference reflected in the curvature of the indifference curve and the interest rate in the intertemporal budget constraint. People can save now to consume in the future or can borrow against expected future income to consume more now. Tobin considered this the origin of the life-cycle model of consumption and saving. Buiter (2003, F590-F591) rightly characterized Tobin’s 1967 contribution to Ten Economic Studies in the Tradition of Irving Fisher as “quite remarkable,” treating “household births and deaths using the Yaari-Blanchard uncertain lifetimes approach” of Yaari (1965)5 and Blanchard (1985) and considering “the extent the life-cycle can, without a bequest motive, account for the kind of savings rates we see in the US. Tobin’s answer is that it can account for most or all of it.” (Buiter, 2003, F590-F591) Closing the model with a neoclassical production function, Tobin endogenized the interest rate. Buiter observes that “The empirical methodology employed is an early example of simulation using calibration”6 and concludes that “With only a modicum of hyperbole, one could describe Tobin as the methodological Godfather of the RBC [real business cycle] school and methodology of Kydland and Prescott (1982)!”

10Tobin and Dolde (1971), in an article they described as a sequel to Tobin (1967), modelled channels of monetary and fiscal influence on consumer behavior, taking account of liquidity constraints (dropping Fisher’s assumption of perfect credit markets in which consumers could borrow or lend at the same interest rate), while Dolde and Tobin (1983) used numerical, calibrated OLG models to consider the macroeconomic consequences of mandatory retirement saving. Tobin (1972), contributing to a festschrift for psychological economist George Katona, paid more attention to consumer surveys (pioneered by Katona) to explore the relationship among wealth, liquidity and the propensity to consume, but Tobin’s articles with Dolde, like his lectures, placed life cycle modelling of consumption and saving in an OLG framework. Tobin was enthusiastic and adept in using an OLG approach in which he considered to be its appropriate field of applicability, life cycle saving and intergenerational wealth transmission. In his teaching and research, and in selecting landmark articles for reprinting in Tobin (2002), Tobin responded favorably to the OLG analyses of Diamond (1965), Yaari (1965), and Cass and Yaari (1966). His objection to Wallace’s OLG explanation of the existence and value of fiat money was not an objection to thinking in terms of overlapping generations models but an objection to what he saw as a misuse of OLG thinking, one that required arbitrary imposition of what he mildly termed the “slightly ridiculous” assumption that no other stores of value existed.

3. Tobin and the Microeconomic Foundations of Macroeconomics

  • 7 Regarding the scale of this literature, notice that one of the chapter titles in E. R. Weintraub (1 (...)

11Tobin viewed his work as “A General Equilibrium Approach to Monetary Theory” (the title of Tobin, 1969; see also Tobin, 1982; Tobin with Golub, 1998). His approach to general equilibrium and optimizing microeconomic foundations is not that of DSGE models (see, inter alia, S. Weintraub, 1957; Harcourt, 1977, E. R. Weintraub, 1979;7, Duarte and Lima, 2012; Cherrier and Saïdi, 2018; Ingrao and Sardoni, 2019; Dimand, 2014; 2020; 2022; Boianovsky, 2022; Ingrao, 2022; Renault, 2022). But as Robert Solow (2004, 660) stressed, “It is not the general appeal to ‘microfoundations’ that Tobin would have rejected in 1968 or 2002; it is rather the extraordinarily limiting and implausible microfoundations that the literature seems willing to accept”—an example of which would be claiming provide rigorous microeconomic foundations for the existence and positive value of fiat money in an OLG model, but only in one that imposes the assumption no other store of value exists. For Tobin, general equilibrium in monetary economics meant that balance sheet identities and the adding-up constraint that asset demands add up to total wealth are respected and that stocks are consistent with flows. He did not accept that microeconomic foundations required budget constraints specifying that all individuals could sell any quantity of their labor that they wished at the current wage rate, considering that not a recognition of rationality or of budget constraints, but rather as a ploy to exclude involuntary unemployment from the model by assumption without drawing attention to the assumption.

12Solow, perhaps the economist closest to Tobin, characterized Tobin’s approach to monetary economics in his introduction to a journal issue in Tobin’s memory:

The first thing you will notice about ‘A General Equilibrium Approach’ [Tobin, 1969] is that its basic building blocks are net-asset-demand functions, which determine the fraction of total wealth parked in each specified asset as a function of the rates of return on the various assets, plus the ratio of income to wealth (to allow for ‘necessities’ and ‘luxuries’ among assets, and to connect up with current flows) and also many unspecified predetermined variables that make sense in context. The signs of the various partial derivatives are discussed in common-sense terms. There are no optimizing consumers, who maximize the expected present discounted value of infinite utility streams, no Euler equations. (Solow, 2004, 659)

13“So,” asked Solow (2004, 659-660), “where are the ‘microfoundations’? The answer is that they are embedded in those common-sense restrictions on partial derivatives. The usual homogeneity postulates and the adding-up conditions imposed by budget constraints are also built into Tobin’s specifications … The other big difference you will notice between Tobin’s approach and today’s fashion is the absence of a representative agent … One can take it for granted that agents are heterogeneous, because they are.”

14Paul Krugman (2023) wrote that while Tobin

was, obviously, a Keynesian in the sense that he believed that workers can and do suffer from involuntary unemployment, and that government activism, both monetary and fiscal, is necessary to alleviate this evil … Tobin was also a neoclassical economist. That is, he believed that you get important insights into the economy as an arena in which self-interested individuals interact, and in which the results of these interactions can usefully be understood by comparing … But using [neoclassical analysis] well, especially when you’re doing macroeconomics, can be tricky. Why? … it’s all too easy to slip into treating on the part of individuals and equilibrium in the sense of clearing markets not as strategic simplifications but as true descriptions of how the world works … So part of the art of producing useful economic models is knowing when and where to place limits on your neoclassicism. And strategic placing of limits is what Tobinomics is about. (Krugman, 2023, 1-2)

15Although not mentioned by either Solow (2004) or Krugman (2023), Tobin’s attitude to OLG modeling, adopting it where he found it useful and appropriate (for example, to evaluate pension schemes) but rejecting its inappropriate application to explaining the positive value of fiat money, exemplified this approach to economic analysis.

16James Tobin’s critique of the version of general equilibrium analysis presented in New Classical economics and of Neil Wallace’s OLG explanation of the existence and positive value of fiat money was in no way a rejection of rigorous theorizing, of microeconomic foundations, of general equilibrium analysis or the usefulness and insightfulness of overlapping generations models, although it was taken as such in the rhetoric identifying rigorous microfoundations with New Classical economics. Tobin’s critique was a rejection of a particularly narrow view of what constituted consistent microeconomic foundations, such as assuming away the possibility on a non-clearing labor market or the existence of stores of value other than fiat money, or using representative agent models (that is, single agent models) to analyze coordination failure. Tobin, whether writing on his own (as in 1967) or with Walter Dolde, found OLG a useful framework within which to continue research on the intertemporal dynamics of saving and consumption that had he studied from his 1947 dissertation onwards. But he had no sympathy whatsoever for basing monetary theory on the assumption that fiat money is the store of value.

I am grateful for helpful comments by Stephen Spear and Warren Young in a session on “OLG-ILA Models, General Equilibrium, and Macroeconomics: Theory and Measurement” at the Society for Economic Measurement conference at the University of Calgary, August 12, 2022. This article is a byproduct of a project on the history of the Cowles Commission and Foundation.

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Notes

1 In Yaari’s case, not just a colleague but a coauthor with Tobin at that time: Cass and Yaari (1966) was reprinted as Cowles Foundation Paper No. 240, immediately preceding No. 241 by Solow, Tobin, von Weizsäcker, and Yaari (1966) on “Neoclassical Growth with Fixed Factor Proportions.” Cherrier and Saïdi (2018, 429) note that Cass had already developed his interest in OLG modeling while working with Yaari at the Cowles Foundation, before being recruited to the University of Pennsylvania by Karl Shell in 1974.

2 Baumol and Tobin (1989) acknowledged that their square-root rule for transactions demand for households had been anticipated by Allais (1947, 238-241). They did not mention, and presumably did not know, that Edgeworth (1888) had already derived a square-root rule for demand for reserves by banks. Edmond Malinvaud (1986; 1987) found the OLG model of Samuelson (1958) anticipated at length in Allais (1947, Appendix II, 640-755), something overlooked even by such close readers of Allais’s mathematical appendix as his students Malinvaud and Gerard Debreu until Malinvaud found it looking for a suitable festschrift topic. As summarized by Malinvaud (1987), Allais considered cases where the wealth of young consumers was equal to labor income (with two possible stationary equilibria, with a positive or negative interest rate depending of whether land is privately or publicly owned), where the wealth of young consumers is equal to national income (one equilibrium with zero interest rate), and where the wealth of young consumers is equal to the sum of rents and labor income (two stationary equilibria, one with a zero interest rate, the other with a positive interest rate due to strong consumer preference for the present). Allais (1962) pointed out that the golden rule of optimal capital accumulation of Edmund Phelps (1961), then a Yale assistant professor and recent Yale PhD, was also in the mathematical appendix of Allais (1947). It is perhaps relevant to these instances of unnecessary originality that the only copy of Allais (1947) in the Cowles Foundation Library is a fiftieth-anniversary reprint that Allais inscribed and gave to James Tobin.

3 As a Yale undergraduate, Peter Diamond worked with Tjalling Koopmans (see Diamond et al., 1962; Koopmans et al., 1964) before going to study with Samuelson and Solow at MIT. In addition to Diamond having worked with Koopmans in the period leading to the Ramsey-Cass-Koopmans approach to optimal capital accumulation (see Koopmans, 1960; 1965), Diamond (1965) was shaped by his graduate training at MIT, particularly by Samuelson (1958) and by Solow, and by his time teaching public economics at the University of California at Berkeley from 1963 to 1965 (see Moscarini and Wright, 2007, 548-549). MIT was a leading center of optimal growth theory in the mid-1960s (see the MIT conference proceeds published as Shell, 1967), which is presumably why Diamond, who had already entered the optimal growth literature as a student and coauthor of Koopmans, went, with Koopmans’s support and encouragement, to MIT for graduate school. Solow et al. (1966) exemplifies the close partnership in neoclassical growth theory between MIT and Cowles economists at that time.

4 Then as now, economists were less conscious of Fisher’s The Rate of Interest (1907) and usually unaware that the celebrated Fisher diagram of optimal smoothing of consumption over two periods is only in the 1907 book, not that of 1930, where intertemporal consumption-smoothing is analyzed verbally (see Dimand, 2019). However, Tobin and Dolde (1971, 99) noted that “The basic idea goes back to Fisher (1907; 1930).” See also Tobin’s introduction to the reprint of Fisher (1906) in Fisher (1997).

5 Tobin (1967) did not cite Yaari (1965) or indeed, apart from mention of Fisher (1930, Chapter V), anything apart from the life cycle articles of Franco Modigliani and his coauthors Albert Ando and Richard Brumberg.

6 Simulation using calibration was undertaken actively at Yale following the arrival of Guy Orcutt as a visiting professor in 1969 and then from 1970 as A. Whitney Griswold Professor of Urban Studies. Because Orcutt’s DYNASIM and MASS microanalytic simulation models had heterogenous agents, they anticipated agent-based modeling (ABM) and heterogenous agent New Keynesian models (HANK) more closely than the representative agent modeling of Kydland and Prescott (see Orcutt et al., 1961; 1976; Orcutt, 1990).

7 Regarding the scale of this literature, notice that one of the chapter titles in E. R. Weintraub (1979) is “The 4,827th reexamination of Keynes’ system.”

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Robert W. Dimand, « James Tobin on Overlapping Generations Models and the Microeconomic Foundations of Macroeconomics Reconsidered »Œconomia, 14-1 | 2024, 21-37.

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Robert W. Dimand, « James Tobin on Overlapping Generations Models and the Microeconomic Foundations of Macroeconomics Reconsidered »Œconomia [En ligne], 14-1 | 2024, mis en ligne le 01 mars 2024, consulté le 23 mai 2024. URL : http://0-journals-openedition-org.catalogue.libraries.london.ac.uk/oeconomia/16900 ; DOI : https://0-doi-org.catalogue.libraries.london.ac.uk/10.4000/oeconomia.16900

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Robert W. Dimand

Department of Economics, Brock University. rdimand@brocku.ca

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